An argument i had with a friend followed this question:
"Given two dice were rolled, and one of them rolled a 3. What would you bet the other dice rolled?"
The phrasing is just to enhance that there might be some number that has an higher probability of showing on the other dice. One of us said that since 7 is the most likely number to be rolled by two dices, then 4 should be the answer. The other said that once the 3 was set on one dice, we should not be looking at anything other than the other cube – so any number would be an equal guess.
Best Answer
This kind of question is very sensitive to how the roller decides what to say. Maybe the dice are different colors and he will tell you the number on the green die. You know nothing about the other die, so all numbers are equally probable. Maybe he will tell you the higher number. Now the only rolls possible are $13,23,33,31,32$ so you should bet on $1$ or $2$. Maybe he will pick a random die and tell you the number on it. Now he could have rolled $33$ and been forced to say $3$ or rolled $3x$ or $x3$ and chosen to say $3$. You have the same chance of $x$ as $3$ for the other die so bet on anything you like. If you don't know how the roller chooses what to say it is not a mathematical question. There is not enough information to answer.